If you're playing on the PlayStation 5, you can find Warzone 2.0 by going to the Modern Warfare 2 store page, then looking in the context menu where different editions of MW2 can be found. Warzone 2.0 should be one of these editions! The same should be the case for the PlayStation 4.
To fix Warzone Season 2 not working or launch on PC, PS5, PS4, or Xbox, users should: Make sure all updates have been installed. Booting into the game while patches are still being downloaded will lock you out of the online portions of the game. Ensure that all updates are downloaded and installed before booting up.